Abstract

We confirm the Aubert-Baum-Plymen conjecture for part of the tempered dual of the p-adic group SL(4). This requires some very detailed representation theory. Of special interest is the case of SL(4,Q_2). Here, there is a tetrahedron of reducibility, and the extended quotient performs a deconstruction: it creates the ordinary quotient and six unit intervals. The six intervals are then assembled into the six edges of a tetrahedron, and create a perfect model of reducibility. The L-packets in this article all conform to the L-packet conjecture in http://eprints.ma.man.ac.uk/1504.